Fractals: Julia sets colored

by Antonio Sánchez Chinchón

Create colored flowers inspired in the Julia Set.

Made with tidyverse, colourlovers

Blog post explaining the experiment: Flowers for Julia

# Load packages
library(tidyverse)

# library(devtools)
# install_github("leeper/colourlovers")
library(colourlovers)

# Choose parameters for your flower
exp <- 6 # exponent of the function
ind <- 0.4785 # independent term of the function
ite <- 7 # number of iterations

# Pick a top palette from COLOURLovers  
pal <- clpalette(1098589) %>% swatch %>% .[[1]] %>% unique() %>% colorRampPalette()


# The function
f <- function(x, y) x^exp + ind

# Reduce approach to iterate
julia <- function (z, n) Reduce(f, rep(1,n), accumulate = FALSE, init = z)

# This is the grid of complex: 3000x3000 between -2 and 2
complex_grid <- outer(seq(-2, 2, length.out = 3000), 1i*seq(-2, 2, length.out = 3000),'+') %>% as.vector()

# Iteration over grid of complex
complex_grid %>% sapply(function(z) julia(z, n=ite)) -> datos


# Build the data frame to do the plt (removing complex with INF modulus)
df <- data_frame(x=Re(complex_grid), 
                 y=Im(complex_grid), 
                 z=Mod(datos)) %>% 
  filter(is.finite(z)) %>% 
  mutate(col=cut(z,quantile(z, probs = seq(0, 1, 1/10)), include.lowest = TRUE))

# Limits of the data to frame the drawing
Mx=max(df$x)+0.2
mx=min(df$x)-0.2
My=max(df$y)+0.2
my=min(df$y)-0.2

# Here comes the magic of ggplot
df %>% 
  ggplot() + 
  geom_tile(aes(x=x, y=y, fill=col, colour = col)) + 
  scale_x_continuous(limits = c(mx, Mx), expand=c(0,0))+
  scale_y_continuous(limits = c(my, My), expand=c(0,0))+
  scale_colour_manual(values=pal(10)) +
  theme_void()+
  coord_fixed()+
  theme(legend.position = "none") -> plot

plot

Compiled: 2019-04-19